Mr Adams has repeatedly denied being a member of the terrorist organisation -- despite accusations from senior politicians, including Taoiseach Enda Kenny.
It has now emerged that Sinn Fein is to directly complain to CNN over its description of the Louth TD.
The party stated that Mr Adams's spokesman has lodged the complaint with CNN's representative in Belfast over how the broadcaster described the party president.
During the World Report programme, Mr Adams was also described as "the leading Catholic politician in Northern Ireland".
The broadcast itself was focusing on the recent loyalist flag protests.
Last night alone three men, including a 17-year-old and a 70-year-old, were arrested during violence in east Belfast.
Mr Adams has been repeatedly challenged for his constant denials of IRA leadership.
Along with senior politicians from most of the mainstream parties, Mr Adams has been accused of playing a senior role in the terrorist organisation by a raft of former Provos.
In September, he was accused of "hiding in the Dail" to dodge questions about the IRA's murder of missing mother-of-10 Jean McConville.
Former IRA bomber Dolours Price has described how Mr Adams ordered her to ferry hostages, including Ms McConville, across the border to be murdered.
Taoiseach Enda Kenny has also challenged Mr Adams over the claims in recent weeks.
"I would love to hear you speak the truth about some elements of your past," he said in the Dail last month.
"You might some day tell the truth about the tragedy and the remorse and about the compassion that should have been shown for Jean McConville.
"Maybe you might do that, Deputy Adams," he added.
His FG colleague and Limerick councillor, Diarmuid Scully, is the latest figure to call on Mr Adams to finally "come clean" on his past.
"If Gerry Adams is willing to be described as such in the international media, why does he continue to deny his former IRA membership here in Ireland.
"Surely the people deserve to know the truth about those who represent them," he said.